arXiv research

The abstract presents a new theorem using Ross-Witt Nyström correspondence and Berndtsson's theorem.

In this paper, we study the Nystr{ö}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{ö}m type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretica…

Study weak geodesic lines in Kähler metric space, disproving a conjecture.

New metric spaces for geodesic rays in cohomology classes.

Paper develops a new kernel approximation framework.

Introduces non-Archimedean metrics for pseudoeffective classes on Kähler manifolds.

In this paper we model the problem of learning preferences of a population as an active learning problem. We propose an algorithm can adaptively choose pairs of items to show to users coming from a heterogeneous population, and use the obtained reward to decide which pair of items to show next. We provide computational…

We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We formulate two convex optimization problems to jointly learn the metric and the clas…

New findings on convexity of special Lagrangian geodesics.

Adapts deep learning with kernel methods for efficient learning.

This work improves knowledge distillation by transferring full kernel matrices efficiently.

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…

Survey of kernels, RKHS, and their applications in machine learning.

In this paper, we study large-scale convex optimization algorithms based on the Newton method applied to regularized generalized self-concordant losses, which include logistic regression and softmax regression. We first prove that our new simple scheme based on a sequence of problems with decreasing regularization para…

We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge regression. Despite its simplicity, the algorithm we study is the first to achieve the op…

Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …

Generalizes uniformization to algebraic correspondences.

Study of holomorphic correspondences combining entire maps and Fuchsian groups.

Introduces non-abelian Hodge correspondence linking algebraic structures to geometry.

New geometric proof for rational tangles links-quivers correspondence.

The paper defines a category of Lagrangian correspondences in super Hilbert spaces and constructs a functorial field theory.

With respect to the Dolbeault complex over the flat manifold $\C^n$, an explicit description of the inverse correspondence of the twistor correspondence is given.

Constructs correspondences on hyperelliptic surfaces combining orbifold groups and Blaschke products.

The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…

Study Kobayashi-Hitchin correspondence for special sheaves on Kähler manifolds.

Constructs Lagrangian correspondences for Higgs bundles and holomorphic connections.

The paper extends Riemann-Hilbert correspondence to foliations.

ROBOT framework solves regression without correspondence for large data and complex models.

The main result of this paper is a discrete Lawson correspondence between discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. This is a correspondence between two discrete isothermic surfaces. We show that this correspondence is an isometry in the following sense: it preserves the metric coefficients int…

In this paper, we define the corresponding submanifolds to left-invariant Riemannian metrics on Lie groups, and study the following question: does a distinguished left-invariant Riemannian metric on a Lie group correspond to a distinguished submanifold? As a result, we prove that the solvsolitons on three-dimensional s…

Overview of dynamics in algebraic correspondences and their connections.

Taxicab correspondence analysis visualizes sparse text data sets.

Proves Giroux Correspondence in 3D using Heegaard splittings.

We demonstrate an isomorphism between the homology of the strand algebra of bordered Floer homology, and the category algebra of the contact category introduced by Honda. This isomorphism provides a direct correspondence between various notions of Floer homology and arc diagrams, on the one hand, and contact geometry a…

In this paper, we want to construct a one-to-one correspondence from the set of diffeomorphism classes of spin $d$-twisted homology $\mc P^3$ to the set of isotopy classes of the embedding from $S^3$ to $S^6$, which is a generalization of the Montgomery-Yang correspondence. Furthermore, we will apply this generalized c…

We show Mckay correspondence of Betti numbers of Chen-Ruan coho- mology for omnioriented quasitoric orbifolds. In previous articles with M. Poddar [8], [9], we proved the correspondence for four dimension and six dimensions. Here we deal with the general case.

Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.

New correspondence links fluxless to fluxy flag manifolds via T-duality.

We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. We give applications to calculations of Floer cohomology, displaceability of Lagrangian correspond…

A neural architecture learns and refines graph correspondences.

For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain.

The Kobayashi-Hitchin correspondence is proven for twisted vector bundles on Kähler manifolds.

We construct examples of singular self-dual Zollfrei metrics explicitly, by patching a pair of Petean's self-dual split-signature metrics. We prove that there is a natural one-to-one correspondence between these singular metrics and a certain set of embeddings of $RP^3$ to $CP^3$ which has one singular point. This embe…

An integral hyperbolic lattice is called reflective if its automorphism group is generated by reflections, up to finite index. Since 1981, it is known that their number is essentially finite. We show that K3 surfaces over C with reflective Picard lattices can be characterized in terms of compositions of their self-corr…

The paper explains geometric correspondences for homothetic navigation.

Correspondence found between exponential families and affine Grassmannians.

Holonomies match for higher local systems and principal 2-bundles.

Study proves correspondence for special bundles on complex surfaces.